There are some (not all) gay men who are fans of Cher, Judy, Liza, and Barbra. The men who happen to be gay who happen to be fans of Cher love her for some of the reasons that librasoul outlined. Plus, in Moonstruck Cher played a character who reinvented herself and changed her life despite the disapproval of family and friends. She was true to herself and made herself happy. Some gay men can relate to that. She also got Nic Cage at the end, and all sorts of people including some gay men like him. That's what I have heard.
My boyfriend who is not gay loves Cher. He perks up everytimes he hears her music or sees her on tv. It's really cute.